In recent years, there has been a renewed and increasing
interest in the study of boundary value problems involving linear and nonlinear integro-differential operators.
This growing interest is fueled both by important applications and seminal advances in the
understanding of nonlocal phenomena from a PDE point of view, see e.g.
[1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]} and the references therein.
Among nonlocal operators of positive differential order, fractional powers of the Laplacian are receiving the most attention.
Recall that, for \(s\in (0,1)\) , the fractional Laplacian of a function \(u \in C^\infty _c(\mathbb {R}^N)\)  is defined by
\(\mathcal {F}((-\Delta )^su)(\xi ) = |\xi |^{2s}\widehat{u} (\xi )\qquad \text{for all $\xi \in \mathbb {R}^N$},\) 
